A method for manufacturing a flame tube for a turbomachine, the said flame tube extending about an axis and comprising an annular radially internal wall and an annular radially external wall, connected to each other by an end wall, the internal wall, the external wall and the end wall defining an internal volume, at least one part of the said end wall forming a double wall comprising a first part and a second part connected to each other and spaced apart from each other so as to delimit a flow channel for a flow of cooling air exiting into the said internal volume, the said flow channel comprising at least one air-inlet opening, the first and second parts of the double wall being connected by connecting zones or bridges extending into the flow channel for the cooling-air flow, at least one connecting area or bridge comprising at least a first conical or flared area, located on the side of the first part and a second conical area or flared area, located on the side of the second part, the second conical area or flared area having a larger flare angle than the flare angle of the first conical area or flared area the method comprising:
- manufacturing the said flame tube by additive manufacturing.